A QECC \(\mathcal {Q}\)  of length \(n\)  is a \(K\) -dimensional subspace of \(q^n\) -dimensional Hilbert space \((\mathbb {C}^{q})^{\otimes n}\) , where \(\mathbb {C}\)  represents complex field and \((\mathbb {C}^{q})^{\otimes n}\)  is the \(n\) -fold tensor power of \(\mathbb {C}^q\) .
Three basic parameters can be used to describe \(\mathcal {Q}\) : length \(n\) , dimension \(k\)  and minimum distance \(d\) , so that \(\mathcal {Q}\)  can be denoted as \([[n,k,d]]_{q}\) , where \(k=log_{q}K\) .
With [1]}, there is a relationship between QECCs and classical dual-containing linear codes under Hermitian inner product.
